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James scored 30 points, Ray Allen had another big game against his old team and the Miami Heat got their first playoff sweep in the Big Three era, advancing to the Eastern Conference semifinals with an 88-77 victory over the Milwaukee Bucks on Sunday.

“It was our next big step as far as our growth,” James said. “It’s so hard to win on the road in the playoffs, in someone’s building — especially when someone is playing for their last life. It’s a big step for us.”

And now the Heat have some much-needed time to rest. Dwyane Wade sat out Sunday’s game, only the second post-season game he’s missed in his career, because of his aching right knee. But with Miami not playing until next Saturday, at the earliest, he’ll have plenty of time to treat the three bone bruises that caused him to miss six games near the end of the regular season.

Miami plays the winner of the Brooklyn-Chicago series. The Bulls lead that series 3-1, with Game 5 on Monday night in New York.

“It’s big,” Wade said of the time off. “Obviously, we’re one of the oldest teams in the league, maybe the oldest team in terms of rotation players. Guys have some bumps and bruises coming out of this series, so it’s going to be great to get some rest. But also we have to take this time to continue to stay sharp, to continue to stay in shape as well.”

Judging by the clinical way in which the Heat dissected the Bucks in this series, that isn’t likely to be a problem.

The defending NBA champions won each game by double digits, getting contributions from their stars and subs alike. Allen finished with 16 points, the third time in the series he scored in double figures, and was 4 of 7 from 3-point range.

Udonis Haslem added 13 points and five rebounds, and Mario Chalmers kicked in eight rebounds and six assists for Miami, which never trailed Sunday.

“They had the whole package,” Bucks coach Jim Boylan said. “When you can afford to sit guy like Dwyane Wade and perform at the level they performed at, that’s a championship-calibre team.”

Monta Ellis led the Bucks with 21 points, and Larry Sanders had 11 rebounds to go with seven points.

But Milwaukee got almost nothing again from Brandon Jennings, who didn’t even play in the fourth quarter. Jennings, who had guaranteed the Bucks would win the series in six games, finished with three points on 1-of-7 shooting.

After scoring 26 points in Game 1, Jennings had 27 total in the final three.

“Frustrated, a little down because I came into this season with so much confidence,” he said. “I thought we had a chance to steal a game in Game 1, Game 2. We let that slip away from us. Game 3, we came back home. Had a 10-point lead, lost that. I mean it’s frustration all around.”

The Heat had chances to sweep their first-round series in each of the last two seasons, taking 3-0 leads on Philadelphia (2011) and New York (2012). But they couldn’t close it out, losing Game 4 each year.

That wasn’t going to happen against the Bucks. Even with Wade reduced to a spectator.

Wade got treatment “around the clock” the last two days in hopes of playing Sunday, and he tested his knee before the game. But he and the Heat decided it wasn’t worth risking aggravating the injury further, and he spent the entire game on the bench in his warmups.

“He gave me the nod saying he wasn’t going to go, so I knew had to pick it up a little more and try to bring us home, bring this win home for us,” James said.

That he did, adding eight rebounds, seven assists and three steals to his 30 points.

“We just space the floor and see if they can stop him. If not, he knows where we are,” Allen said. “We just give him that room to operate.”

The Heat led by as many as 11 in the first half, only to see the Bucks steadily chip away at the lead. When Mike Dunleavy drained a 3 and Ellis scored on a floater, it cut Miami’s lead to 69-67 with 9:34 to play.

Ellis was fouled by Allen on the play, but he missed the free throw and James grabbed the rebound. He fed Allen, who knocked down — what else, a 3. J.J. Redick missed a long 3 and James found an open Chalmers for another 3 that gave the Heat a 75-67 lead with 8:27 left.

The 3 was Chalmers’ 80th in the post-season, tying Tim Hardaway’s franchise record.

After Luc Richard Mbah a Moute made the second of two free throws, James scored on a layup. Redick made a jumper, but Shane Battier and Allen closed out the Bucks with a pair of 3s. James then converted a three-point play and added a layup to complete the 19-5 run — a spurt in which he had a hand in every single Miami score.

“At some point during that stretch right there, he decided he was going to put his imprint on the game and he did. In a big way,” Boylan said. “When you’re a superstar player like he is, that’s what superstar players do.”

NOTES: The Heat have won eight straight post-season games dating to last season. That matches the franchise record. … NBA Commissioner David Stern was in attendance. … James scored 30 or more for the 54th time in the post-season, second only to Kobe Bryant among active players. … Milwaukee had seven of its 16 turnovers in the first quarter. … The Bucks are now 20-26 in elimination games. … Packers LB Clay Matthews was at the game.

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